Porous media: the Muskat problem in 3D

TL;DR

This paper investigates the 3D Muskat problem, focusing on the Rayleigh-Taylor condition and initial interface topology to establish local existence results in Sobolev spaces.

Contribution

It provides new insights into the conditions ensuring local existence of solutions for the 3D Muskat problem, emphasizing the role of interface topology and stability criteria.

Findings

Rayleigh-Taylor condition is crucial for well-posedness

Topology of initial interface affects solution existence

Local existence proven in Sobolev spaces

Abstract

The Muskat problem involves filtration of two incompressible fluids throughout a porous medium. In this paper we shall discuss in 3-D the relevance of the Rayleigh-Taylor condition, and the topology of the initial interface, in order to prove its local existence in Sobolev spaces.